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If [tex][tex]$g(x)=\frac{x+1}{x-2}$[/tex][/tex] and [tex][tex]$h(x)=4-x$[/tex][/tex], what is the value of [tex][tex]$(g \circ h)(-3)$[/tex][/tex]?

A. [tex][tex]$\frac{8}{5}$[/tex][/tex]
B. [tex][tex]$\frac{5}{2}$[/tex][/tex]
C. [tex][tex]$\frac{15}{2}$[/tex][/tex]
D. [tex][tex]$\frac{18}{5}$[/tex][/tex]

Sagot :

GinnyAnswer
To find the value of [tex]\((g \circ h)(-3)\)[/tex], we will follow these steps:

1. Evaluate [tex]\( h(-3) \)[/tex]:
- Given [tex]\( h(x) = 4 - x \)[/tex], substitute [tex]\( x = -3 \)[/tex]:
[tex]\[ h(-3) = 4 - (-3) = 4 + 3 = 7 \][/tex]

2. Evaluate [tex]\( g(h(-3)) \)[/tex]:
- We know [tex]\( h(-3) = 7 \)[/tex]. Now, we need to find [tex]\( g(7) \)[/tex], where the function [tex]\( g(x) \)[/tex] is given by [tex]\( g(x) = \frac{x+1}{x-2} \)[/tex]:
[tex]\[ g(7) = \frac{7 + 1}{7 - 2} = \frac{8}{5} \][/tex]

Thus, the value of [tex]\((g \circ h)(-3)\)[/tex] is [tex]\(\frac{8}{5}\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{\frac{8}{5}} \][/tex]
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